This simulation study examines the characteristics of the Explanatory Item Response Model (EIRM) when estimating treatment effects when compared to classical test theory (CTT) sum and mean scores and item response theory (IRT)-based theta scores. Results show that the EIRM and IRT theta scores provide generally equivalent bias and false positive…

Building on prior research on the relationships between key concepts in item response theory and classical test theory, this note contributes to highlighting their important and useful links. A readily and widely applicable latent variable modeling procedure is discussed that can be used for point and interval estimation of the individual person…

Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of…

Since Cronbach's (1951) elaboration of a from its introduction by Guttman (1945), this coefficient has become ubiquitous in characterizing assessment instruments in education, psychology, and other social sciences. Also ubiquitous are caveats on the calculation and interpretation of this coefficient. This article summarizes a recent contribution…

The aim of this simulation study, determine the relationship between true latent scores and estimated latent scores by including various control variables and different statistical models. The study also aimed to compare the statistical models and determine the effects of different distribution types, response formats and sample sizes on latent…

In spite of all of the technical progress in observed-score equating, several of the more conceptual aspects of the process still are not well understood. As a result, the equating literature struggles with rather complex criteria of equating, lack of a test-theoretic foundation, confusing terminology, and ad hoc analyses. A return to Lord's…

The problem of factor score indeterminacy implies that the factor and the error scores cannot be completely disentangled in the factor model. It is therefore proposed to compute Harman's factor score predictor that contains an additive combination of factor and error variance. This additive combination is discussed in the framework of classical…

A jack knife is a pocket knife that is put to many tasks, because it's ready to hand. Often there could be a better tool for the job, such as a screwdriver, a scraper, or a can-opener, but these are not usually pocket items. In statistical terms, the expression implies making do with what's available. Another simile, of an extreme situation, is…

Three decision consistency and accuracy (DC/DA) methods, the Livingston and Lewis (LL) method, LEE method, and the Hambleton and Han (HH) method, were evaluated. The purposes of the study were: (1) to evaluate the accuracy and robustness of these methods, especially when their assumptions were not well satisfied, (2) to investigate the "true"…

The purpose of this study was to develop general outcome measures (GOM) in mathematics so that teachers could focus their instruction on needed prerequisite skills. We describe in detail, the manner in which content-related evidence was established and then present a number of statistical analyses conducted to evaluate the technical adequacy of…